Philosophy of Science
What science is, how it advances, and how different philosophical approaches understand it, alongside the statistical and methodological foundations that ground research practice. Concise topics you can scan and expand inline.
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Philosophy of Science Approaches
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- What Is Science?What distinguishes science from other kinds of knowledge?
- The Scientific MethodThe cycle of observation, hypothesis, test and revision
- The Problem of InductionHume's challenge to reasoning from past to future
- The Hypothetico-Deductive MethodDeriving testable consequences from hypotheses
- The Demarcation ProblemWhat separates science from pseudoscience?
- PositivismKnowledge only from observable facts
- Logical Positivism (Vienna Circle)Verifiability as the criterion of meaning
- Falsificationism (Popper)Science advances by attempts to refute, not to confirm
- Paradigms and Scientific Revolutions (Kuhn)Normal science, anomaly, crisis and paradigm shift
- Scientific Research Programmes (Lakatos)Hard core, protective belt, progressive vs degenerating programmes
- Epistemological Anarchism (Feyerabend)"Anything goes": there is no single scientific method
- Scientific Realism and Anti-RealismDo theories describe the world, or merely work?
- Scientific Explanation (the DN Model)Explanation as deduction of the event from laws
- Bayesian Philosophy of ScienceDegrees of belief updated by evidence
- Research ParadigmsPositivism, interpretivism, pragmatism, critical realism
- Reproducibility and Open ScienceThe replication crisis, preregistration and transparency
Statistical & Methodological Foundations
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- Hypothesis: Null and AlternativeThe logic of statistical hypothesis testing
- The Central Limit TheoremWhy the sample mean tends toward a normal distribution
- Sampling MethodsProbability and non-probability sampling
- Statistical Significance and the p-valueWhat the p-value does and does not tell you
- Type I and Type II ErrorsFalse positives, false negatives and power
- Statistical Errors and BiasSampling error, non-sampling error, bias vs variance
- Confidence IntervalsInterval estimation and its correct interpretation
- Effect SizeThe magnitude of an effect, independent of sample size
- Descriptive vs Inferential StatisticsSummarizing data vs generalizing to a population
- Variable Types and Levels of MeasurementNominal, ordinal, interval, ratio
- Validity and ReliabilityThe two core dimensions of measurement quality
- Correlation vs CausationAssociation does not imply causation
- Measures of Central TendencyMean, median and mode
- Measures of DispersionHow spread out the data are
- Skewness and KurtosisThe shape of a distribution
- Foundations of ProbabilityEvents, conditional probability and Bayes
- The Normal DistributionThe bell curve and z-scores
- Common Probability Distributionst, F, chi-square, binomial, Poisson
- The Sampling DistributionHow a statistic varies across samples
- Standard Error vs Standard DeviationTwo often-confused quantities
- Degrees of FreedomThe number of values free to vary
- Parametric vs Non-parametric TestsWhich family of test, and when
- Statistical AssumptionsNormality, homogeneity, independence
- One-tailed vs Two-tailed TestsDirectional vs non-directional hypotheses
- The Multiple Comparisons ProblemMany tests inflate false positives
- Bootstrapping and ResamplingInference without distributional assumptions
- Bayesian vs Frequentist InferenceTwo philosophies of statistics
- Statistical Power and Sample SizeThe chance of detecting a real effect
- Choosing the Right Statistical TestA practical test-selection guide
- Missing Data MechanismsMCAR, MAR, MNAR
- Outliers and Influential ObservationsDetecting and handling them sensibly
- Data Transformation and StandardizationLog, square-root, z, min-max
Statistical Literacy
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- Sensitivity and SpecificityHow well a test catches positives and negatives
- Predictive Values (PPV and NPV)The real probability given a test result
- ROC Curves and AUCThreshold-independent classifier performance
- The Confusion MatrixThe basis of all classification metrics
- Classification Metrics: Accuracy, Precision, Recall, F1Evaluating a classifier correctly
- Likelihood RatiosHow a test result updates the odds
- Cohen's d and the Standardized Mean DifferenceThe magnitude of a difference between two means
- Variance Explained: Eta-squared and R-squaredHow much variability the model explains
- The Odds RatioA measure of association for categorical outcomes
- Relative Risk and Risk DifferenceComparing risk as a ratio and as a difference
- Number Needed to Treat (NNT)How many patients for one extra good outcome
- The Hazard RatioComparing instantaneous risk over time
- Measures of Association for Categorical DataEffect size after a chi-square test
- Overfitting and UnderfittingA model's ability to generalize
- The Bias-Variance TradeoffThe tension between two sources of error
- Training, Validation, and Test SetsSplitting data for honest evaluation
- RegularizationPreventing overfitting with a penalty
- Model Selection and Information CriteriaChoosing among competing models
- Goodness-of-Fit and Model ErrorHow well a model fits the data
- Regression DiagnosticsChecking the assumptions of a regression
- Interaction EffectsWhen one effect depends on another variable
- Random VariablesMapping outcomes to numbers
- Expected Value and VarianceA distribution's centre and spread
- The Law of Large NumbersWhy the sample mean converges to the truth
- Bayes' TheoremUpdating beliefs in light of evidence
- Joint, Marginal, and Conditional DistributionsHow several variables behave together
- How to Conduct a Hypothesis TestThe step-by-step testing procedure
- Checking Statistical Assumptions in PracticeWhat to do when assumptions fail
- Reporting Statistical ResultsReporting findings fully and honestly
- Interpreting p-values, Confidence Intervals, and Effect Sizes TogetherReading the whole picture, not one number
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